Evaluation of the German Annuities Market 070503 Uni

SONDERFORSCHUNGSBEREICH 504
Rationalitätskonzepte,
Entscheidungsverhalten und
ökonomische Modellierung
No. 03-08
Surprises in a Growing Market Niche - An Evaluation
of the German Private Annuities Market
Hans-Martin von Gaudecker∗
and Carsten Weber∗∗
May 2003
Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of
Mannheim, is gratefully acknowledged.
∗ Mannheim
Research Institute for the Economics of Aging, email: [email protected]
∗∗ Sonderforschungsbereich
504, email: [email protected]
Universität Mannheim
L 13,15
68131 Mannheim
Surprises in a Growing Market Niche
An Evaluation of the German Private Annuities Market
Hans-Martin von Gaudecker *)
Carsten Weber **)
Abstract
High replacement rates from public old age insurance might lead to the belief that little room
is left for private sector annuities in Germany. Taking a closer look, we find a small market
with a surprisingly large variety of products. Due to the recent pension reform and future
ones to come the market is projected to grow substantially in the upcoming years. This paper
describes the available annuity contracts and determines their money’s worth for different
subgroups of the population.
*) Mannheim Research Institute for the Economics of Aging, Department of Economics,
University of Mannheim
**) Institute of Insurance Science and Department of Business Administration, University of
Mannheim
We would like to thank Axel Börsch-Supan and Anette Reil- Held for the impulse for this
paper and many helpful comments, the latter also applies fully to Peter Albrecht and
Alexander Ludwig. Finally we appreciate data provision by Thomas Lueg from GDV. Any
remaining flaws are the authors’ sole responsibility.
1.
Introduction
Annuities generate a life- long income stream in return for a premium paid to an insurance
company. In their simplest form they provide protection against the risk of outliving one’s
resources by pooling the assets of persons with similar life expectancies when longevity is
uncertain. They are viewed as the most important decumulation device in private defined
contribution schemes. In Germany, tax relief for third pillar savings introduced by the 2001
pension reform is only granted if a specified fraction is annuitized no later than at the age
of 85.
Markets for annuities all over the world are smaller tha n predictions from economic theory
suggest. 1 The literature proposes several explanations for this phenomenon. Wherever
applicable, crowding out due to public defined benefit systems is probably the most important
reason. In a sense, payments from these schemes can be viewed as annuities. Other
possibilities include adverse selection if consumers are better informed about their survival
probabilities than insurers; loss of liquidity; unwillingness to surrender one’s capital to an
insurance company due to psychological reasons or stemming from a bequest motive; and
administrative loads or possible mark-ups from providers. 2 Some of these may lead to the
assertion that annuities include high load factors from the perspective of the consumer. A load
factor is any difference between the premium charged by an insurer and the premium that
would have to be paid for a hypothetical actuarial fair annuity. In our later discussion, we
define it to be one minus the money’s worth Ratio.
The most popular approach to estimate these load factors has been pioneered by
Warshawsky (1998). He defines the Money’s worth ratio (MWR) as the expected discounted
present value of all future payments from the annuity contract, divided by the premium
payment and calculates its values for the US market. The difference between the MWR and
one is the proportional loading charge as perceived by the consumer. Mitchell et al. (1999)
refine this concept and use more recent data for the US. They also extend the analysis into
several directions, for example they incorporate taxes and calculate the insurance value of
annuities for a class of CRRA utility functions. James and Vittas (2001) apply the money’s
worth methodology to several countries and discuss policy implications which emerge from
interna tional experiences. Mitchell and McCarthy (2002) review this literature in the light of
1
2
See Mitchell and McCarthy (2002) for an overview.
See for example James and Vittas (2001)
-2-
world-wide demographic change and supply discussions of various annuities-related topics,
such as differential mortality and regulatory issues.
To our knowledge, such an analysis has not yet been carried out for Germany. Public old age
benefits have traditionally been very high, but they are projected to decline and the need for
private provision of old age security will rise. This paper addresses the question of whether
the German annuities market is prepared to provide reasonable substitutes for public
payments in terms of product types and load factors. Our findings are encouraging. Despite its
small size, a wide variety of annuity products exists. The MWR ranges between 0.65 and 1.1
depending on the assumptions one is ready to make. Our preferred assumptions yield an
approximate value of 0.95, which fits in well with international comparisons. Furthermore,
specifically elaborated mortality tables are an important prerequisite for the functioning of
annuities markets. These exist for Germany but they will need to be improved in the future.
The paper is organized as follows. Section two tries to sketch the current size of the German
annuities market and describes the expectations regarding its future development. Section
three characterizes the products available in the market and points out the ones which are
analyzed later on. Section four contains a description of the mortality tables commonly used
by insurance companies. In the fifth section we determine the money’s worth of commonly
available annuities and present some comparative statics as well as a comparison with
international findings. Conclusions are drawn in the last section.
2.
Market Overview
This section tries to outline the size of the German annuities market. Data are scarce due to its
relatively small size compared to other insurance markets. We use publications from the
Association
of
German
Insurance
Companies
(Gesamtverband
der
deutschen
Versicherungswirtschaft, GDV), which comprise virtually all commercial insurers in the
period from 1998 to 2001. The data are aggregated at a level which includes some minor
figures that do not fit in well with our definition of annuities, for example invalidity insurance
and long term care insurance. The figures shown thus are higher than true values but they
should be reasonably close to them.
Table 1 shows the payouts from annuities as compared to payments made from the public old
age insurance system, which are the major source of income during retirement in Germany.
-3-
Their importance is still small, rising from a level of 1% in 1998 to 1.5% in 2001. Total
payouts ranged at 2,735 Mio Euro in 2001, this is a rise of about 58% in a three year period.
Future increases are projected to be even higher. First, reductions of public pension payments
are likely to generate a new demand for private pension plans. Second, the 2001 pension
reform has created tax incentives to invest in private pension plans which include mandatory
annuitization no later than at the age of 85. 3
Unfortunately, no figures on the accumulation side of private old age provision by means of
annuity contracts are available. The reason for this is the aggregation level of the data: most
products of German life insurers serve different purposes and we are not able to isolate the
ones of interest to us. Consider for example an endowment policy which facilitates both
annuitization and lump sum withdrawal of the accumulated stock. In order to analyze these
figures we would need the share of policies being annuitized which is not available.
3.
Product Overview
Despite its relatively small size a wide variety of contracts is offered in the German annuities
market. Sections 3 and 5 draw upon the data base “LV-Win“ from Morgen & Morgen GmbH,
Hofheim am Taunus. It is a standard product used by brokers to make offers to their clientele.
Thus insurance companies have a strong interest in the correct representation of their products
and fees. The sample contains 80 companies and covers about 95% of the market. It does not
include any group insurance (“Kollektivversicherungen”), e.g. through employer-sponsored
pension plans.
For the contracts under consideration, we are not able to link offers with sales. This would be
most interesting because we find large differences in both product design and prices, which
might be inconsistent with rational informed consumer behavior. Exploring their actual
purchasing patterns could provide some important insights. However, the data are sufficient to
evaluate the money’s worth of individual annuities. Extending the typology of Poterba (1997),
we first organize the products along the following lines.
Method of paying premiums: The two predominant forms in this category are fixed annual
and single premiums (“Rentenversicherung gegen laufende Beiträge” / “RV gegen
Einmalzahlung”). We do not have information on the availability of more flexible
3
Quoted from Schnabel (2002), where a detailed analysis of future prospects of the German annuities market
can be found.
-4-
contribution schemes. Our focus in the analysis below is on single premium annuities, the
motivation will be given in the next paragraph.
Waiting period: Contracts with zero and positive waiting periods should be distinguished in
an analysis. Nonetheless our focus on single premium immediate annuities (SPIAs,
“sofortbeginnende RV gegen Einmalzahlung”) is quite general because most deferred
annuities (“aufgeschobene RV”) contain a refund option during accumulation. 4 In this case, a
person approaching retirement age faces exactly the same choice regarding annuitization as
someone who accumulated stock in a different investment object. Consequently, such a
contract can be divided into two different components, the first one being an accumulation
vehicle, the second one being a SPIA. For our purposes only the latter part is of interest.
Number of lives insured: An individual life annuity pays benefits to the recipient until the
time of death. In case of a joint annuity, payments continue as long as any of the insured
persons is alive. With very few exceptions only individual contracts are offered on the
German market. However, depending on the above contract characteristics some 65-78% of
the companies offer supplementary survivorship insurance (“Hinterbliebenenzusatzversicherung”) which has the same implications as a joint annuity. We only consider
individual contracts as neither data on prices for survivor policies nor joint mortality tables
are available.
Nature of payouts: We consider period certain annuities (“RV mit Garantiezeit”) and life
annuities without refund (“RV ohne Beitragsrückgewähr”). In the first case benefits are paid
during a fixed number of years regardless of the death of the annuitant. If he dies, the
payment is made to his beneficiaries. Period certain annuities are more popular than regular
ones. The longest possible guaranteed payment period depends on the entry age, with no
guaranteed payment possible beyond the age of 80. We include periods of 0, 5, 10, 15, and 20
years, although we report only results on the 0 and the 10 year period certain contracts.
Roughly a third of the companies offer contracts with a refund option during the
decumulation phase. We do not consider these products for clarity reasons.
Allocation of investment and inflation risk: Three combinations are possible in this case. Real
annuities assign both risks to the insurer. He bears the investment risk only if the annuity is
4
This is true for 96% of the contracts offered on the market with fixed annual premiums and 86% of single
premium deferred annuities.
-5-
paid on a nominal basis and none of the two if a variable annuity is considered. 5 We could not
detect any real annuities offered on the German market. There exists a small but growing
market of pure variable annuities (“fondsgebundene RV”). Their money’s worth will depend
in large parts on the future returns on the underlying investment vehicle. 6 Although we will
face a similar problem when evaluating standard German annuity contracts, it is less
important there. We do not consider variable annuities in our analysis.
The standard product in Germany is a participating annuity. It contains a nominal guaranteed
annuity and a variable part which depends on the surplus of the company. 7 Law restricts the
maximum interest rate insurers can use to calculate the guaranteed part of the annuity to
3.25%. It further requires firms to apply mortality tables and costs valid on the date when the
contract was signed. The nominal guaranteed annuity is calculated on this basis. Capital gains
or losses on the annuitants’ assets relative to this rate as well as deviations of realized from
expected mortality and administrative costs enter the surplus of the company. If positive, at
least 90% of the capital gains have to be paid out to the insured within 5 years according to
tax law. 8 On the basis of their surplus, companies calculate the profit sharing rate
(“Überschussbeteiligung”). Subtracting the guaranteed rate of generally 3.25% and
multiplying this by the initial premium payment yields the variable, or participating,
component of the annuity.
Type of participation: The two polar forms of participation are constant and escalating
schemes (“Konstante Rente” and “Dynamische Rente”). Most companies also offer mixed
forms (“Teildynamische Rente”). If participation of the constant type is chosen, each year an
amount depending on the premium payment and the profit sharing rate is added to the
guaranteed part. If this rate does not change over time, the annuity will be constant, however
it can either rise or fall over time. With the escalating annuity option the participation
component is annuitized, yielding a yearly rise of the guaranteed pension payment. This
annual growth rate (“Dynamisierungsfaktor”) equals approximately the profit sharing rate less
the guaranteed interest rate of usually 3.25%.
Throughout the last 25 years variations of the profit sharing rate have been very low
compared to capital market fluctuations: German insurance companies follow a strategy of
5
One might argue that a variable annuity provides a hedge against inflation. In our case the validity of the
Fisher effect is not required, as we do not include inflation in the analysis.
6
For a description of the mechanics of variable annuities, see Poterba (1997).
7
The following description of the German participation scheme is a gross simplification. For details on the
system, see for example Schierenbeck and Hölscher (1998).
8
See Schierenbeck and Hölscher (1998), p. 734.
-6-
smoothing surplus over time. Tax law facilitates this by allowing hidden reserves in the
balance sheet. Additionally, high periodic surpluses can be used to build up reserves which
have to be distributed in the course of up to five years. Albrecht and Maurer (2002) consider
the net investment returns of insurers on a book value basis. Since this is the predominant and
most volatile position in the surplus (minor ones being gains or losses from actual over
expected mortality and costs) this is a reasonable proxy for profit sharing rates. Average net
investment returns ranged between 6.85% and 7.5% during the period from 1980 to 1998 for
the thirty largest insurers. 9 More recently, profit sharing rates already declined slightly to a
2002 average of 6.17%. In 2003 they experienced another drop to currently 4.8%10 which
represents an all time low. These figures contain the guaranteed interest rate of 3.25%.
4.
Mortality tables
This section illustrates some rather technical details regarding the mortality tables available in
Germany. It contains additional information which is not essential for understanding the
money’s worth concept in the succeeding section and might be skipped. We follow the
calculation
of
tables
provided
by
the
German
Actuaries’
Society
(Deutsche
Aktuarvereinigung, DAV), labeled DAV 1994 R. To our knowledge these provide the
calculation base for most insurance companies when dealing with annuities. Some large
insurers are known to construct their own tables while small companies lack the sufficient
database to do so. In the following we try to outline the method of construction as done in
Schmithals and Schütz (1995). The last part of this section compares the different tables and
comments on their validity for our purposes.
Schmithals and Schütz (1995) consider four basic steps to construct the annuitant mortality
tables which we use for estimating the money’s worth ratios of annuities: first, a trend
function is estimated which approximates future mortality changes. In a next step, period
tables are constructed for each year. Cohort mortality can be derived directly from these
tables. 11 Fourth, mortality differences between the general population and insured persons are
calculated, yielding two different tables. In order to reflect actuarial conservativeness, the
final DAV 1994R tables contain an arbitrary further reduction of mortality in a fifth step. This
one is irrelevant for us because it has nothing to do with actual mortality.
9
Albrecht and Maurer (2002).
Average profit sharing rates refer to all firms in the market and were provided by Morgen & Morgen GmbH.
11
For a nice introduction on this matter, see McCarthy and Mitchell (2002)
10
-7-
Estimation of the trend function: For this purpose, census data from 1870 to 1987 are used to
obtain a log- linear regression function. In the recent past sharper declines in old age mortality
than before are detected. In order to take this into account, a multiplicative bonus in old age
mortality improvements is incorporated into the trend function. This results in a constant
mortality decline over time for each age group. Trend functions differ by sex but are assumed
to be identical for annuitants and members of the general population.
Construction of period tables: Using the trend function, a period table obtained from census
data is projected into each future year under consideration. Additionally, a smoothing
algorithm is applied and the tables are extrapolated to cover mortality until age 110 because
census tables end at age 89.
Construction of cohort tables: In order to obtain cohort mortality, a generation is “followed”
through the period tables. The resulting tables are often referred to as two-dimensional tables.
Mortality tables for the insured population: With data from six life insurance companies
ranging from 1967 to 1992 the relative mortality of insured persons to the general population
is calculated, depending on sex and age. Consistent with adverse selection a lower mortality
of annuitants is detected.
Comparison of the different tables: McCarthy and Mitchell (2000) provide some metrics for
comparing mortality tables, out of which we only report small parts. Figure 1 shows annual
probabilities of death, conditional on reaching the respective year of life. It clearly reveals
higher mortality for men relative to women. Of course, rates for the insured population are
lower than for the general population. Table 2 shows the expected remaining lifetime at
age 65. The calculations from period tables can be interpreted as the expected remaining
lifetime of a contemporary 65-year-old if there were no mortality improvement for his cohort
in the future. The difference between two row entries thus yields the effect of the trend
function for his cohort. Differences between column entries show the effect of switching from
the general to the insured population.
Comment on the tables: A few critical notes seem necessary regarding these mortality tables.
First, one can always dispute the validity of past time trends for predicting future mortality
improvements. Another approach would be to model expected medical change and simulate
-8-
its impact on expected future mortality. 12 We stick with the standard approach of the DAV
because it seems reasonable in an international perspective. 13 The way mortality differences
between the general population and annuitants are constructed does not make sense for our
purposes. This issue arises because the sample size of insured persons is very small, having a
minimum for females aged 60 to 65 with about 20 observed deaths. The resulting relative
mortality of insured women aged 60 is 110% compared to 47% at the age of 62. Clearly, this
does not make sense. Schmithals and Schütz (1995) help themselves by assuming the relative
mortality of this group to be 40% lower for insured persons relative to the general population.
While being sufficiently conservative in order to calculate premiums, this approach does not
consistently estimate the relative mortality of insured persons. Lacking better data we use
these tables anyways. Collecting adequate data on annuitant mortality will be necessary.
Therefore, our results for the annuitant population thus should be seen as an orientation only
regarding the magnitude of the selection effects. A more serious problem stems from the lack
of data on mortality beyond age 89. As explained above, the 2001 pension reform
incorporates the possibility of programmed withdrawals and deferred annuitization at the age
of 85. Current data clearly are not sufficient for calculating fairly priced annuities in this
group.
5.
The Money’s Worth of Individual Annuities
In this section we apply the methodology developed by Mitchell et al. (1999) to determine the
load factors in the German market, looking at single premium immediate annuities as
described in section three. To get an idea of the magnitude of the monthly payouts, we first
present their averages, maxima, and minima per € 1,000 premium in tables 3 and 4.14
Reported results are from samples of 17 to 61 firms, because not every firm offers the whole
range of contract specifications. 15 Consistent with international findings, 16 we discover
considerable price heterogeneity among firms. Correlations between profit sharing rates and
guaranteed payouts are positive in a range from 0.25 to 0.3. This means that on average there
is no trade-off between the two, which might have been a reason for payout heterogeneity, if
risk aversion varies across consumers. If there had been a trade-off, a highly risk averse
12
For example, GE Frankona Re bases its reinsurance products for annuities on an approach like this. See GE
Frankona Re (2000).
13
See McCarthy and Mitchell (2000).
14
All our calculations are based on an initial premium of € 100,000. Contrary to our expectations based on
administration loads, increasing this value produces a slight decrease in the payout ratio and vice versa.
15
For our purposes sample size does not matter since we are only interested in the availability of products.
16
See Mitchell and McCarthy (2002) for the US, James and Vittas (2001) for the UK, Australia, and Canada.
-9-
consumer might have chosen a contract with high guaranteed payments and less important
participating components, the opposite being true for consumers with lower risk aversion.
Examining the link between annuity payouts and the rating of providers, we also detect some
positive correlation. Thus, there is no risk premium implicit in the contracts but pricing seems
to depend on factors unobservable for us.
Due to differential mortality, average payouts increase with the entry age and payouts for men
are considerably higher than for women at each age. Surplus payouts are almost equal across
age and sex groups on an individual contract level, suggesting that they only depend on the
initial premium. Thus the variable part of the annuity is more important for women than for
men as they face a lower guaranteed payout. This is also true for younger persons compared
to older ones. Findings on period certain annuities are not surprising either. We only report
values for the 10- year period, which yields lower payouts than a contract without such an
attribute. The difference in payouts between regular and period certain annuities increases
with the entry age because of increasing mortality.
The Money’s Worth Methodology: To illustrate loading charges we calculate the Money’s
worth ratio (MWR) which is defined as the expected discounted value of future payouts from
the insurance company per Euro of premium. All monthly benefit payments are multiplied by
the probability of reaching the corresponding month of life (i.e. the probability of receiving
this payment), discounted, summed up and divided by the initial premium:
1
MWR =
⋅
Pr emium
T p ⋅A
t t
t
t =1 (1+i t )
∑
At this point three parameters are to be determined: the interest rate for a t- month investment
it , the survival probability up to period t pt , and monthly payouts At . Regarding the mortality
assumptions, we use the tables discussed in the preceding section17 . To obtain monthly
survival probabilities, we calculate the geometric mean of annual values. This amounts to
assuming constant probabilities within years of life. Second, to discount future benefits, we
use short-term Euro- money- market rates and the yields of German government bonds
(“Staatsanleihen”) for maturities of one to thirty years. The latest maturity on the German
treasury market is 26.8 years. After this period we update this interest rate into the future. Last
17
For readers who have skipped this section, there is one table for the general population and another one for
insured persons with lower mortality rates. This is due to adverse selection: people with short remaining life
expectancies do much less frequently buy immediate annuities.
- 10 -
and most important are the insurance payouts. We calculate MWRs for the guaranteed
nominal annuity only and for the two polar participation schemes. The corresponding
assumptions are described in detail in the following paragraphs, a comparative static analysis
follows at the end of this section. Finally, we incorporate guaranteed payment periods in the
analysis. This amounts to assuming a survival probability of one during the period of
guaranteed payouts, afterwards the same formulas apply as in the simple case. We only report
results for 10-year period certain annuities, as MWRs do not vary substantially across
different periods.
Discussion of the discount rate: A major determinant of the MWR is the discount rate which
has to reflect an alternative investment with similar risks attached to it. In the case of pure
nominal annuities, this risk is restricted to the insolvency risk of the annuity provider. This led
researchers in other countries to using the corporate bond yields as discount rates. 18 We
neglect this risk because of the strong regulatory framework in Germany. There has not been
any reported insolvency of an insurance company for decades. Even without default risk,
German annuities bear some investment risk for the participating part. Using government
yields will overstate the MWR if there is no risk adjustment. However, applying yields of the
Markovitz market portfolio will overestimate the attached risk. As the product profile is
unique, an adequate rate simply does not exist. A look at the low historical volatility of net
investment returns on a book value basis of life insurers favors the use of government
yields. 19 This procedure is disputable and the reader not comfortable with it is referred to the
comparative static analysis.
Results for Germany: Consider the first column in Panel I of table 6. It contains MWRs only
for the guaranteed nominal annuity assuming zero participation in all periods. This is clearly a
drastic assumption, but it provides some insight because the insurer bears investment and
mortality risk only up to this point. The first entry shows the MWR for 60-year-old males,
assuming population mortality. Its value of 0.76 appears to be rather low, but apart from the
interest rate, assumptions are as conservative as possible. Results for ages 60 and 70 are
similar. Looking at the outcomes for annuitants, we find a selection effect which raises the
MWR by 0.07 to 0.09 points. This is about the magnitude encountered in international
18
19
See Mitchell and McCarthy (2002) for a good discussion.
This implies using portfolio volatility as perceived by the consumer as risk measure.
- 11 -
comparisons 20 . Nevertheless it should be interpreted with caution due to the problems
associated with the corresponding mortality table.
For the second column we use 2003 payouts of contracts with the constant participation
scheme and simply update them into all future periods. We will return to the plausibility of
this assumption later. Ratios rise to 0.89 and more. The increase is most pronounced for 60year-olds, because as noted earlier the absolute value of the participation payment only
depends on initial premiums. This group has the highest remaining life expectancy. The
selection effect rises proportionally compared to the first column. For annuitants the MWR
approaches unity.
In order to obtain MWRs for the escalating participation scheme we use the same growth
rates of the annuities for all periods as reported in our data base for 2003 for each insurer.
MWRs are slightly lower than for the constant participation scheme. In this case the selection
effect becomes more pronounced because high benefits in late periods are weighted stronger
due to lower mortality among annuitants.
With regard to Panel II, we do not expect notable changes of the MWR for the annuitants.
Turning the life annuity into a certain payment during ten year period should be reflected in a
reduction of payouts which is based on annuitant mortality. Our results confirm this
expectation. Correspondingly, MWRs for the general population rise slightly by 0.01 to 0.04
points because setting mortality to zero during ten years results in a larger difference for this
group. Hence, the selection effect can be attenuated by including a guaranteed payment
period.
Results for women are reported in Table 7. MWRs are higher in most cases, around 0.78 for
the guaranteed annuity in the general population. The selection effect seems to be less
important than for males, ranging form 0.05 to 0.075 in the first column. Incorporating any
participation component produces stronger increases in the MWR than in the case of males
which is due to lower female mortality. Again, the participation component only depends on
the initial premium, not on sex or age. Nearly all values including participation payments
exceed unity. Conclusions regarding period certain annuities are the same as for males.
Comparative Statics: Our results depend heavily on the assumptions on interest and profit
sharing rates. Up to now we assumed values given today which need not be valid in the
20
An overview is given in Mitchell and McCarthy (2002).
- 12 -
future. In this section we explore alternative scenarios and relate them to past experiences. We
consider increases in either one or both rates. Similar results are obtained for corresponding
decreases, thus we do not report them.
Tables 8 and 9 show some results if 100 or 200 basis points are added to either the annual
interest or the profit sharing rate, or both. Raising the interest rate by 100 basis points
produces drops in MWR of the guaranteed part of 0.05 to 0.07 (see the first column in
Panels II). The effect gets weaker when increasing the entry age. This last statement is also
true for relative changes, which is nearly equal in all three columns. An increase in the
interest rate of 100 basis points causes the money’s worth to fall by 6.3% to 8.3%. The effect
is strongest for women aged 60 and least pronounced for 70-year-old males. It declines in the
magnitude of the basis points added to the interest rate, see Panel V. These figures show how
important interest rate assumptions are for the MWR.
When varying the profit sharing rates, we only consider changes in the annuities’ growth rates
in the escalating scheme. We did not find a reasonable way to model the impact of changes in
profit sharing rates on benefits in the constant participation scheme. The relative changes are
slightly larger in absolute value than in the case of the interest rate. Adding 100 basis points to
the profit sharing rate in each period yields a rise of the MWR of 7.8% to 13.5%. The large
range stems from mortality differences and the calculation of the participation component. As
expected, it is highest for the group with the lowest mortality rate which are female annuitants
aged 60. A 70-year-old man belonging to the general population profits the least from such a
rise. 21
Increasing both rates by 100 basis points at the same time yields MWRs similar to the ones
resulting from our original assumptions (see Panels IV). If they are increased by 200 basis
points each, the profit sharing rate effect predominates and causes higher MWRs.
The assumptions which lead to our original results under either the constant or the escalating
participation scheme seem most plausible to us. The profit sharing rates we use are
historically low and they appear sufficiently conservative even in the current capital market
situation, although they certainly do not represent a lower bound. During the last 20 years,
insurers have been more successful than this. Another assumption one may want to criticize is
the interest rate level, which is also low in a historical perspective. This might yield too high
21
The gains would be closer together in the case of constant participation. See the above discussion of the
selection effect in the different participation schemes.
- 13 -
MWRs. However, if they were to increase we would suspect a positive correlation of interest
and profit sharing rates. 22 In this case, either scenario IV or VI might apply and results do not
change substantially.
International comparisons: Our results fit in well with international findings as compiled in
Mitchell and McCarthy (2002) from different sources. We report them in Table 10. MWRs
based on our preferred assumptions for both annuitant and general populations are
comparable to those estimated in the UK, Australia and Italy, while being slightly lower than
in Canada and higher than in the US. Nevertheless, it should be noted that these values are
estimates for guaranteed nominal annuities, while our analysis is based on participating
annuities. This does not imply direct utility consequences if consumers are willing to bear
some risk. After all, there is the possibility to gain more through the participation component,
which is not present in pure guaranteed annuities. Estimates for the MWR of participating
annuities are available for Switzerland. They are remarkably high, exceeding unity for almost
all subgroups of the population. In our understanding of the original paper by James and
Vittas (2001), these are based on rather optimistic assumptions on the participation
component. Results are comparable to those reported in the third Panels of Tables 8 and 9,
which reflect the scenario present a few years ago.
The insurance value of annuities: We use the results from Mitchell et. al. (1999) to illustrate
the utility value for a CRRA utility function with a unity risk aversion parameter. This reflects
a relatively low risk aversion. They assume stochastic inflation with a mean of 3.2% and a
preexisting real annuity amounting to 50% of total wealth at the age of 65, e.g. claims from
public old age insurance. For different values of the interest rate and the individual time
discount rate, they obtain critical MWR values of about 0.75. This is to be interpreted as
follows: an individual with this utility function who already owns a real annuity will attach a
positive utility value to an additional nominal annuity if the loading charges do not exceed
25%. Comparing this result to tables 8 and 9, we find that he will buy an additional annuity in
nearly all of the scenarios, even if only considering the guaranteed part of the annuity.
22
Bonds are the predominant capital investment of insurance companies. As future coupon payments go up
because of rising interest rates, so should profit sharing rates.
- 14 -
6.
Summary and Outlook
Our findings thus far came as a positive surprise to us. Money’s worth ratios in Germany are
comparable to international ones despite the small market size. Consumers can choose among
many different contract specifications, although we are missing offers of real annuities and
offers for people older than 70. The decline of benefits from the public old age insurance
scheme and tax benefits for private retirement saving will lead to an increase in volume. It is
not clear, however, what will happen to money’s worth ratios if annuities account for a
significant part of insurance companies’ revenue in the future. They might increase because of
fiercer competition. On the contrary, if companies have some market power, MWRs could
decrease because annuities have to account for a larger revenue share.
Mortality tables will need improvement in order to facilitate sensible pricing of annuities with
an entry age of 85 years which are projected to be a popular withdrawal option for third pillar
saving. From our perspective, a better estimation of the selection effect is desirable.
- 15 -
References
Albrecht, Peter and Raimond Maurer (2002), Self-Annuitization, Consumption Shortfall in
Retirement and Asset Allocation: Journal of Pension Economics and Finance 1 (3),
November: 269-288.
GDV, Gesamtverband der Deutschen Versicherungswirtschaft e.V. (2002, 2001, 2000),
Statistical Yearbook of German Insurance. Karlsruhe: Verlag Versicherungswirtschaft.
GE Frankona Re (2000), Langlebigkeit und Le ibrenten: Die Rückversicherungslösungen der
GE Frankona Re. Munich.
James, Estelle and Dimitri Vittas (2001), Annuities markets in comparative perspective: Do
consumers get their money's worth? In: OECD 2000 Private Pensions Conference. Paris:
OECD.
McCarthy, David and Olivia Mitchell (2000), Assessing the Impact of Mortality Assumptions
on Annuity Valuation: Cross-Country Evidence. Pension Research Council Working Paper
2001-3. The Wharton School, University of Pennsylvania.
McCarthy, David and Olivia Mitchell (2002), International Adverse Selection in Life
Insurance and Annuities. Pension Research Council Working Paper 2002-8. The Wharton
School, University of Pennsylvania.
Mitchell, Olivia and David McCarthy (2002), Annuities for an Ageing World. NBER
Working Paper 9092. National Bureau of Economic Research, Cambridge, MA.
Mitchell, Olivia, James Poterba, Mark Warshawsky, and Jeffrey Brown (1999), New
Evidence on the Money’s Worth of Individual Annuities. American Economic Review,
December: 1299-1318.
Poterba, James (1997), The History of Annuities in the United States. NBER Working
Paper 6001. National Bureau of Economic Research, Cambridge, MA.
Schierenbeck, Henner and Reinhold Hölscher (1998), Bank Assurance. Stuttgart: Schäffer
Poeschel, 4th ed.
- 16 -
Schmithals, Bodo and Esther Schütz (1995): Herleitung der DAV-Sterbetafel 1994 R für
Rentenversicherungen. Blätter der Deutschen Gesellschaft für Versicherungsmathematik
XXII, April: 29-69.
Schnabel, Reinhold (2002), Annuities in Germany before and after the Pension Reform of
2001. CeRP Working Paper 27/02. Center for Research on Pensions and Welfare Policies,
Torino.
Warshawsky, Mark (1988), Private Annuities Markets in the United States. Journal of Risk
and Insurance, September: 55(3), 518-528.
- 17 -
Table 1
1
2
3
Annuities
paid by
insurers
Main
insurance
benefits paid
by insurers
Year
Mio Euro
Mio Euro
1998
1999
2000
2001
1,732
2,053
2,457
2,735
Increase 1998-2001
Average annual
Increase
Payments
from Public Growth Rate
Old Age
Annuities
Insurance
Ratio
Ratio
Mio Euro
1/2
1/3
25,841
29,402
32,804
35,429
171,512
167,782
177,758
183,393
6.7%
7.0%
7.5%
7.7%
1.0%
1.2%
1.4%
1.5%
57.9%
37.1%
6.9%
12.1%
8.2%
1.7%
18.5%
19.7%
11.3%
Note: Main Insurance Contracts denote life insurance contracts, private old age insurance, and some minor
positions. They are called this way because they may include additional options such as invalidity insurance,
which are not included in these figures. Source: GDV, Statistical Yearbooks of German Insurance 2002, 2001,
2000.
Table 2
Expected remaining lifetime
Male
Population
Male
Insured
Female
Population
Female
Insured
Period table for 2003,
beginning at age 65
16.0
18.6
19.9
22.3
Cohort aged 65 in 2003
16.9
19.6
21.3
24.1
Note: Own calculation based on tables provided in Schmithals and Schütz (1995).
- 18 -
Table 3
Payouts per € 1.000 Premium – Men
No Period Certain Annuity
Guaranteed
Part
Constant
Participation
Scheme
Average
60 Lowest
Highest
4.84
4.72
4.99
5.72
4.73
6.33
Average
65 Lowest
Highest
5.51
5.38
5.71
6.43
5.45
7.00
Average
70 Lowest
Highest
6.68
6.47
6.90
7.59
6.47
8.18
10 Years Period Certain Annuity
Guaranteed
Part
Constant
Participation
Scheme
Average
60 Lowest
Highest
4.73
4.50
4.90
5.55
4.64
6.19
Average
65 Lowest
Highest
5.30
5.04
5.50
6.07
5.25
6.75
Average
70 Lowest
Highest
6.17
5.86
6.39
6.96
6.02
7.54
Note: Annuity payouts as provided in LV-Win by Morgen & Morgen GmbH.
Calculations are based on an initial premium of Euro 100,000 on a single
premium immediate life annuity.
- 19 -
Table 4
Payouts per € 1.000 Premium – Women
No Period Certain Annuity
Guaranteed
Part
Constant
Participation
Scheme
Average
60 Lowest
Highest
4.27
4.17
4.42
5.18
4.19
5.75
Average
65 Lowest
Highest
4.91
4.74
5.08
5.79
4.74
6.35
Average
70 Lowest
Highest
5.69
5.54
5.89
6.57
5.54
7.12
10 Years Period Certain Annuity
Guaranteed
Part
Constant
Participation
Scheme
Average
60 Lowest
Highest
4.23
4.04
4.39
5.06
4.16
5.70
Average
65 Lowest
Highest
4.82
4.59
5.00
5.62
4.67
6.25
Average
70 Lowest
Highest
5.49
5.22
5.70
6.31
5.36
6.88
Note: Annuity payouts as provided in LV-Win by Morgen & Morgen GmbH.
Calculations are based on an initial premium of Euro 100,000 on a single
premium immediate life annuity.
- 20 -
Table 5
Term
1 Month
3 Months
6 Months
1 year
2 years
3 years
5 years
7 years
10 years
15 years
20 years
25 years
30 years
Interest Rate
2.65%
2.53%
2.46%
2.41%
2.33%
2.49%
3.06%
3.61%
4.00%
4.36%
4.55%
4.75%
4.76%
Source: European Central Bank, Monthly Bulletin March 2003,
and http://www.bondboard.de/.
- 21 -
Table 6
Panel I - No Guaranteed Payment Period, Men
Age
Mortality
Table
Only
Guaranteed
Part
Constant
Participation
Scheme
Escalating
Participation
Scheme *)
Population
0.763
0.902
0.886
Annuitants
0.833
0.985
0.981
Population
0.760
0.886
0.864
Annuitants
0.840
0.980
0.968
Population
0.780
0.887
0.868
Annuitants
0.872
0.990
0.982
60
65
70
*) Average Growth Rate: 1.55%
Panel II - 10 Years Guaranteed Payment Period, Men
Age
Mortality
Table
Only
Guaranteed
Part
Constant
Participation
Scheme
Escalating
Participation
Scheme *)
Population
0.780
0.915
0.894
Annuitants
0.835
0.980
0.971
Population
0.788
0.902
0.885
Annuitants
0.846
0.969
0.963
Population
0.817
0.921
0.900
Annuitants
0.876
0.988
0.976
60
65
70
**) Average Growth Rate: 1.45%
Note: Each entry shows the Money’s worth ratio. All calculations
use the all-company sample average annuity payouts. Samples differ
by type of contract, this is why average growth rates may differ, too.
- 22 -
Table 7
Panel I - No Guaranteed Payment Period, Women
Age
Mortality
Table
Only
Guaranteed
Part
Constant
Participation
Scheme
Escalating
Participation
Scheme *)
Population
0.776
0.942
0.922
Annuitants
0.826
1.003
0.995
Population
0.795
0.938
0.921
Annuitants
0.857
1.012
1.008
Population
0.795
0.918
0.900
Annuitants
0.870
1.005
0.999
60
65
70
*) Average Growth Rate: 1.55%
Panel II - 10 Years Guaranteed Payment Period, Women
Age
Mortality
Table
Only
Guaranteed
Part
Constant
Participation
Scheme
Escalating
Participation
Scheme *)
Population
0.782
0.935
0.917
Annuitants
0.827
0.988
0.982
Population
0.805
0.940
0.923
Annuitants
0.858
1.001
0.997
Population
0.814
0.936
0.912
Annuitants
0.873
1.004
0.992
60
65
70
**) Average Growth Rate: 1.45%
Note: Each entry shows the Money’s worth ratio. All calculations
use the all-company sample average annuity payouts. Samples differ
by type of contract, this is why average growth rates may differ, too.
- 23 -
Table 8
Comparative Statics - Men, No Guaranteed Payment Period
Panel I
Only
Guaranteed
Part
Age
60
65
70
Panel II
Constant
Escalating
Participation Participation
Scheme
Scheme
Population
0.763
0.902
0.886
Annuitants
0.833
0.985
0.981
Population
0.760
0.886
0.864
Annuitants
0.840
0.980
0.968
Population
0.780
0.887
0.868
Annuitants
0.872
0.990
0.982
70
0.815
0.909
0.901
Population
0.706
0.823
0.798
Annuitants
0.778
0.907
0.891
Population
0.731
0.830
0.809
Annuitants
0.812
0.923
0.911
Basis points added to interest rate:
Basis points added to profit sharing rates:
Only
Guaranteed
Part
Constant
Escalating
Participation Participation
Scheme
Scheme
Population
-
-
0.980
Annuitants
-
-
1.096
Population
-
-
0.941
Annuitants
-
-
1.064
Population
-
-
0.931
Annuitants
-
-
1.063
0
Only
Guaranteed
Part
Age
60
65
70
0
100
Constant
Escalating
Participation Participation
Scheme
Scheme
Population
-
-
0.899
Annuitants
-
-
1.005
Population
-
-
0.867
Annuitants
-
-
0.977
Population
-
-
0.866
Annuitants
-
-
0.983
Basis points added to interest rate:
100
Basis points added to profit sharing rates:
100
Panel VI
Only
Guaranteed
Part
Age
100
Panel IV
Panel V
70
0.834
0.769
0
Basis points added to profit sharing rates:
65
70
0.705
Annuitants
0
Basis points added to interest rate:
60
65
Population
Basis points added to profit sharing rates:
Age
65
60
Constant
Escalating
Participation Participation
Scheme
Scheme
Basis points added to interest rate:
Panel III
60
Only
Guaranteed
Part
Age
Constant
Escalating
Participation Participation
Scheme
Scheme
Population
0.654
0.774
0.753
Annuitants
0.712
0.842
0.832
Population
0.658
0.768
0.741
Annuitants
0.723
0.843
0.825
Population
0.687
0.780
0.758
Annuitants
0.760
0.863
0.848
Basis points added to interest rate:
Basis points added to profit sharing rates:
Only
Guaranteed
Part
Age
60
65
70
200
0
Constant
Escalating
Participation Participation
Scheme
Scheme
Population
-
-
0.917
Annuitants
-
-
1.037
Population
-
-
0.872
Annuitants
-
-
0.991
Population
-
-
0.865
Annuitants
-
-
0.986
Basis points added to interest rate:
200
Basis points added to profit sharing rates:
200
Note: Each entry shows the Money’s worth ratio using the same samples as before. Either a parallel shift is
applied to the interest rate for each period and / or the profit sharing rate is increased in the same fashion.
- 24 -
Table 9
Comparative Statics - Women, No Guaranteed Payment Period
Panel I
Only
Guaranteed
Part
Age
60
65
70
Panel II
Constant
Escalating
Participation Participation
Scheme
Scheme
Population
0.776
0.942
0.922
Annuitants
0.826
1.003
0.995
Population
0.795
0.938
0.921
Annuitants
0.857
1.012
1.008
Population
0.795
0.918
0.900
Annuitants
0.870
1.005
0.999
70
0.846
0.924
0.914
Population
0.733
0.866
0.846
Annuitants
0.790
0.933
0.925
Population
0.738
0.853
0.832
Annuitants
0.805
0.930
0.920
Basis points added to interest rate:
Basis points added to profit sharing rates:
Only
Guaranteed
Part
Constant
Escalating
Participation Participation
Scheme
Scheme
Population
-
-
1.036
Annuitants
-
-
1.130
Population
-
-
1.018
Annuitants
-
-
1.125
Population
-
-
0.978
Annuitants
-
-
1.096
0
Only
Guaranteed
Part
Age
60
65
70
0
100
Constant
Escalating
Participation Participation
Scheme
Scheme
Population
-
-
0.948
Annuitants
-
-
1.036
Population
-
-
0.932
Annuitants
-
-
1.030
Population
-
-
0.901
Annuitants
-
-
1.006
Basis points added to interest rate:
100
Basis points added to profit sharing rates:
100
Panel VI
Only
Guaranteed
Part
Age
100
Panel IV
Panel V
70
0.868
0.761
0
Basis points added to profit sharing rates:
65
70
0.715
Annuitants
0
Basis points added to interest rate:
60
65
Population
Basis points added to profit sharing rates:
Age
65
60
Constant
Escalating
P articipation Participation
Scheme
Scheme
Basis points added to interest rate:
Panel III
60
Only
Guaranteed
Part
Age
Constant
Escalating
Participation Participation
Scheme
Scheme
Population
0.662
0.803
0.780
Annuitants
0.705
0.855
0.844
Population
0.679
0.803
0.780
Annuitants
0.731
0.864
0.853
Population
0.688
0.795
0.772
Annuitants
0.748
0.864
0.851
Basis points added to interest rate:
Basis points added to profit sharing rates:
Only
Guaranteed
Part
Age
60
65
70
200
0
Constant
Escalating
Participation Participation
Scheme
Scheme
Populati on
-
-
0.984
Annuitants
-
-
1.093
Population
-
-
0.946
Annuitants
-
-
1.060
Population
-
-
0.903
Annuitants
-
-
1.017
Basis points added to interest rate:
200
Basis points added to profit sharing rates:
200
Note: Each entry shows the Money’s worth ratio using the same samples as before. Either a parallel shift is
applied to the interest rate for each period and / or the profit sharing rate is increased in the same fashion.
- 25 -
Table 10
International MWRs - 65-year-old Men
Germany
UK
Australia
Canada
Switzerland
US
Italy
Population
0.887
0.897
0.914
0.925
0.965
0.814
not
available
Annuitants
0.980
0.966
0.986
1.014
1.169
0.927
0.958
International MWRs - 65-year-old Women
Germany
UK
Australia
Canada
Switzerland
US
Italy
Population
0.939
0.910
0.910
0.937
1.029
0.852
not
available
Annuitants
1.013
0.957
0.970
1.015
1.152
0.927
0.965
Note: Results for Germany are taken from our own calculations. MWRs for other countries stem from the
compilation given in Mitchell and McCarthy (2002) and from James and Vittas (2001)
- 26 -
Figure 1
Conditional Mortality Rates - Period Table 2000
Mortality Rates
0,5
0,4
0,3
Male Insured
Male Population
0,2
Female Population
0,1
Female Insured
0
60
65
70
75
80
85
90
95
100 105
110
Age
Note: The conditional mortality rate is the probability of dying at age t+1 conditional on reaching age t. Based on
tables provided in Schmithals and Schütz (1995).
Figure 2
Growth Rate Annuities by Company and Average,
Escalating Participation Scheme
3,5
3
Percent
2,5
2
1,5
1
0,5
0
Companies
Note: Growth Rates by company as provided in LV-Win by Morgen & Morgen GmbH.
Figure 2
Interest Rate and Average Participation Rate 2003
(=Growth Rate Annuities + 3.25%)
5
Percent
4
3
2
1
0
0
5
10
15
20
25
30
Years
Note: Average profit sharing rates calculated from growth rates as provided in LV-Win by Morgen & Morgen
GmbH. Interest rates are taken from ECB monthly bulletin, March 2003 and http://www.bondboard.de/.
- 27 -
SONDERFORSCHUNGSBereich 504 WORKING PAPER SERIES
Nr.
Author
Title
03-10
Alain Chateauneuf
Jürgen Eichberger
Simon Grant
Choice under Uncertainty with the Best and Worst
in Mind: Neo-additive Capacities.
03-09
Peter Albrecht
Carsten Weber
Combined Accumulation- and Decumulation-Plans
with Risk-Controlled Capital Protection
03-08
Hans-Martin von Gaudecker
Carsten Weber
Surprises in a Growing Market Niche - An
Evaluation of the German Private Annuities Market
03-07
Markus Glaser
Martin Weber
Overconfidence and Trading Volume
03-06
Markus Glaser
Thomas Langer
Martin Weber
On the trend recognition and forecasting ability of
professional traders
03-05
Geschäftsstelle
Jahresbericht 2002
03-04
Oliver Kirchkamp
Rosemarie Nagel
03-03
Michele Bernasconi
Oliver Kirchkamp
Paolo Paruolo
No imitation - on local and group interaction,
learning and reciprocity in prisoners
break
Expectations and perceived causality in fiscal
policy: an experimental analysis using real world
data
03-02
Peter Albrecht
Risk Based Capital Allocation
03-01
Peter Albrecht
Risk Measures
02-51
Peter Albrecht
Ivica Dus
Raimond Maurer
Ulla Ruckpaul
Cost Average-Effekt: Fakt oder Mythos?
02-50
Thomas Langer
Niels Nauhauser
Zur Bedeutung von Cost-Average-Effekten bei
Einzahlungsplänen und Portefeuilleumschichtungen
02-49
Alexander Klos
Thomas Langer
Martin Weber
Über kurz oder lang - Welche Rolle spielt der
Anlagehorizont bei Investitionsentscheidungen?
02-48
Isabel Schnabel
The German Twin Crisis of 1931
SONDERFORSCHUNGSBereich 504 WORKING PAPER SERIES
Nr.
Author
Title
02-47
Axel Börsch-Supan
Annamaria Lusardi
Saving Viewed from a Cross-National Perspective
02-46
Isabel Schnabel
Hyun Song Shin
Foreshadowing LTCM: The Crisis of 1763
02-45
Ulrich Koch
Inkrementaler Wandel und adaptive Dynamik in
Regelsystemen
02-44
Alexander Klos
Die Risikoprämie am deutschen Kapitalmarkt
02-43
Markus Glaser
Martin Weber
Momentum and Turnover: Evidence from the
German Stock Market
02-42
Mohammed Abdellaoui
Frank Voßmann
Martin Weber
An Experimental Analysis of Decision Weights in
Cumulative Prospect Theory under Uncertainty
02-41
Carlo Kraemer
Martin Weber
To buy or not to buy: Why do people buy too much
information?
02-40
Nikolaus Beck
Kumulation und Verweildauerabhängigkeit von
Regeländerungen
02-39
Eric Igou
The Role of Lay Theories of Affect Progressions in
Affective Forecasting
02-38
Eric Igou
Herbert Bless
My future emotions versus your future emotions:
The self-other effect in affective forecasting
02-37
Stefan Schwarz
Dagmar Stahlberg
Sabine Sczesny
Denying the foreseeability of an event as a means of
self-protection. The impact of self-threatening
outcome information on the strength of the
hindsight bias
02-36
Susanne Abele
Herbert Bless
Karl-Martin Ehrhart
Social Information Processing in Strategic Decision
Making: Why Timing Matters
02-35
Joachim Winter
Bracketing effects in categorized survey questions
and the measurement of economic quantities